Quadrant trigonometric functions fq defined from trigonometric functions f by the relation fq(x)=f(qx), q=π/2 are strongly recommended because of their effectivity in the computation of f for arguments containing π as a factor. By the similar reason, base 2 exponential functions are also recommended for use in place of exponential functions. Wide-spread abuse of inverse matrices for the solution of simultaneous linear equations is accused, and overall cooperation for its prevention is addressed to intelligent audience.

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This paper shows a result of numerical calculation of a one-parameter family of surfaces with constant mean curvature spanning a Wiener contour. The method used here is founded on the theorems of H. C. Wente and K. Steffen concerning solutions to the volume constrained Plateau problem. The augmented Lagrangian method and Uzawa's algorithm are applied. The computed surfaces are classified according to the stability. An unstable minimal surface spanning a Wiener contour is obtained numerically. Considering a container which is filled with gas and has a fixed solid wall and a mouth covered with a free thin film, we state that, when the boundary of the mouth forms a Wiener contour with an appropriate proportion and when the pressure of the gas in the container changes so slowly that the free thin film passes through a succession of equilibrium states, the deformation of the film is discontinuous at some values of the pressure of the gas.

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Empirical studies suggest that scheduling policies for CPU processing and job loading affect the processing capacity of computer systems. These policies use the characteristics of how each job requests hardware resources. This review presents, firstly, the process of how the author has been studying the above scheduling problem. The difficulty of the problem lies in the fact that the general model to which the practical engineers want to have solutions is analytically intractable. Secondly, this review presents some properties of scheduling on the basis of the theoretical results on restrictive but analytically tractable models that may give us a solid understanding of the effect of scheduling on the processing capacity of computer systems. These studies show that the simple CPU scheduling policy whereby I/O bound jobs have preemptive priority over CPU bound jobs is effective and shows sound behavior in all cases. On the other hand, the optimal job loading policy is complicated and its unsuccessful implementation may easily lead to serious performance degradation.

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Information geometry is a new theoretical method to elucidate intrinsic geometrical structures underlying information systems. It is applicable to wide areas of information sciences including statistics, information theory, systems theory, etc. More concretely, information geometry studies the intrinsic geometrical structure of the manifold of probability distributions. It is found that the manifold of probability distributions leads us to a new and rich differential geometrical theory. Since most of information sciences are closely related to probability distributions, it gives a powerful method to study their intrinsic structures. A manifold consisting of a smooth family of probability distributions has a unique invariant Riemannian metric given by the Fisher information. It admits a one-parameter family of invariant affine connections, called the α-connection, where α and-α-connections are dually coupled with the Riemannian metric. The duality in affine connections is a new concept in differential geometry. When a manifold is dually flat, it admits an invariant divergence measure for which a generalized Pythagorian theorem and a projection theorem hold. The dual structure of such manifolds can be applied to statistical inference, multiterminal information theory, control systems theory, neural networks manifolds, etc. It has potential ability to be applied to general disciplines including physical and engineering sciences.

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